In the 16th century, very few people were interested in math and science in general. Only in the 17th century there was a real flourishing of scientific associations of universities independent. The first cases of regular gathering of mathematicians were recorded thanks to Marin Mersenne. In this paper, we will briefly introduce you to the work of Marin Mersenne, his contribution to the theory of numbers, and Mersenne’s numbers. Then we’ll introduce you to numbers of special shapes and features, perfect and amicable numbers. Since the Pythagoreans have attributed certain social qualities to numbers, the numbers that are worthy of being equal to the sum of their true divisors are called perfect numbers. An outstanding contribution to the discovery of perfect numbers of special forms was given by Euclid, Pierre de Fermat and Leonhard Euler. Until now, 51 perfect numbers have been discovered and all are even. Scientists believe that odd perfect numbers do not exist, but nobody has proven it. The other type of numbers studied by the ancient Greeks are amicable numbers. The first rule to find amicable numbers of special form was given by Thabit ibn Qurra. On the basis of his rule, many other rules have been created, among which are the most famous Euler’s rule, Borho’s Rule, Wieathaus’s Rule and te Riele’s Rule. Although more than 1 223 393 596 amicable pairs are known today, scientists have not yet proven that there are infinitely many amicable numbers.